When the clock hands first meet after three

Question

At what time after 3:00 do the hour hand and minute hand of a clock first lie exactly on top of each other?

Short answer

At $3{:}16\tfrac{4}{11}$ , about 3:16:22. The minute hand gains $5.5^\circ$ per minute on the hour hand and starts $90^\circ$ behind, so it catches up after $90/5.5=180/11$ minutes.

Adapted from Crack, Heard on the Street, Q1.12, p.11; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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